Fun with Small Sample Sizes

Submitted by 909Dewey on October 2nd, 2011 at 7:58 PM

Brady Hoke has coached five games at Michigan. Let’s see where Hoke’s games stand in relation to the last few years. I want to use the idea of score dominance to group these last few seasons together and get an idea of dominant performances. I am defining score dominance as the percent of final score, or margin of victory in shutouts. Rodriguez finished three seasons here, and in the interest of historical perspective I will also include Carr’s last three seasons. Counting Hoke’s five games there have been exactly 80 games played since the start of the 2005 season.

UM’s record in that span is 47-33, where Rodriguez is responsible for two thirds of the losses. The worst five games were the 2011 Gator Bowl, 2007 Ohio, 2010 Ohio, 2007 Oregon, and the ultra-horrible 2008 Ohio game where UM managed to gain just .143 of the total score - going down 42-7 in Columbus. The five best games in terms of score dominance are Eastern in 2005 and Notre Dame in 2007 (both shutouts,) the 2006 Indiana game, 2009 Delaware State, and the third shutout in 80 games, 2011 Minnesota. Brady Hoke is responsible for only 6.25% of the last 80 games, yet contributed one third of the shutouts and the most lopsided win. Can that possibly mean anything?

I think so. I do not think it would be reasonable to use Hoke’s record at UM and extrapolate that he will never lose a game. Yet the fact is four of his five games make up four of the 13 most lopsided victories of the recent past. Carr contributed 16% of his games to the top 13 routs, and RR contributed 8% of his contests to the blowout total. A reasonable expectation is that Hoke will have a blowout pace between those two numbers – we will say 12%. He is currently operating at 80%. He is beating expectations almost by a factor of 7.

I am not going to try and predict a win total here, small sample size and all. I do believe that Hoke has this team overachieving in a very big way. I also believe that if that keeps up, and so far there is no indication that it can’t, we are going to see some very special things this year.


turd ferguson

October 2nd, 2011 at 8:02 PM ^

The Hoke sample isn't just small; it's also biased toward lesser opponents.  This would be interesting as a full diary (with charts and all) but probably not until the end of this season.


October 2nd, 2011 at 9:21 PM ^

He's also including RR and Carr's biggest wins against lesser opponents, so it's at least partially apples-to-apples. I think what he's trying to say is that when Hoke has won, the wins have been impressive  - at least as, if not more, impressive than RR and Carr's (in his last years) big wins against lesser opponents.

I think the flaw in these observations is less about sample size, and more about the fact that Hoke inherited a hell of a team from the RR era. We expected to win all of these games. However, I will agree with the OP that the wins are definitely feel-good, and I would like to believe they indicate greater things to come.

turd ferguson

October 2nd, 2011 at 10:06 PM ^

I think the lesser opponent issue makes this kind of claim problematic:

"Brady Hoke is responsible for only 6.25% of the last 80 games, yet contributed one third of the shutouts and the most lopsided win."

Also, I'm not convinced that Hoke inherited a much better team than RR.  It seems like Hoke inherited considerably better offensive talent while RR inherited considerably better defensive talent.  To the extent that it looks like our defensive talent is pretty good right now, I think a lot of that should be attributed to talent development (and better use of that talent) by the new staff.


October 2nd, 2011 at 8:41 PM ^

With five minutes gone in the second quarter yesterday, we were on pace for 900 yards of total offense.  I was a bit disappointed that we couldn't sustain that.

Swayze Howell Sheen

October 2nd, 2011 at 9:33 PM ^

and thought it was going to be about your sex life.

oh I KID, I KID! :)


more seriously, too premature. we're all excited, but taking a huge number of returning starters and getting to 5-0 with wins over a number of cupcakes (and one I think very good ND team) is not a good basis for extrapolation...




October 2nd, 2011 at 9:48 PM ^

While I like our chances against NW because of Persa's injury and NW isn't a particularly intimidating venue, MSU and Iowa are likely to be tough and very physical games at very hostile stadiums.


October 3rd, 2011 at 7:09 PM ^

"and he'd have Ryan Mallett."

Let's beat this to death one more time:  Mallett was gone the moment Mitch Mustain transferred.

Now we can certainly speculate that, had Mustain remained at Arkansas, Rodriguez's arrival would still have prompted Mallett to leave.  We can also speculate that the fact that he couldn't get along with his teammates would have played a role, independent of who his coach was.  But it seems a stretch to state unequivocably that, had Hoke become coach in 2008, he would have had the services of Ryan Mallett at his disposal.